The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions
and | Sep 21, 2017
Published Online: Sep 21, 2017
Page range: 39 - 48
Received: May 27, 2016
Accepted: Jun 29, 2016
DOI: https://doi.org/10.1515/auom-2017-0019
Keywords
© 2017
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
In this paper, by using (h, ϕ)-generalized directional derivative and (h, ϕ)-generalized gradient, the authors directly derives the Karush- Kuhn-Tucker conditions by applying a corollary of Farkas lemma under the Mangasarian-Fromovitz constraint qualification.Furthermore, the boundedness of Lagrange multipliers is showed.